This type of reduction
was proposed by Cardin and Teixera [1]} and algorithmically formalized by Kruff et al. in
[2]}. We call it nested, since
the reduced dynamics at intermediate timescales are embedded
in normally hyperbolic invariant manifolds that form a nested family
(manifolds of slower variables are included in manifolds of faster
variables).
In [1]} both manifolds were considered, the stable and unstable one.
As in [2]} we only consider here the stable case. The stable normally hyperbolic invariant manifolds attract and sequentially confine the dynamics
of the system, with rates from fastest to slowest, and are used to obtain reductions valid at intermediate timescales.
